Do I need to get a new transmission?

I recently blew a head gasket in my 2003 Honda Civic EX and the engine got full of water. I decided to just replace the engine with a different one. I was looking at a K20A 2.0l, which is a vtec. Would I need to replace the transmission for a different one as well? If so, can I please get a list of transmissions if I do?
And if I do just get the original 1.7 vtec can you please put a link for me to the transmission so I can look at it?

If you use the same motor as replacement you wouldn't have to change the transmission. And, being a 2003 Honda civic, it would be cheaper to buy a newer car than to swap both the motor and the trans in the civic.

The transmission is a separate assembly from the engine, damaging the engine would not damage the transmission unless something catastropic and spectacular happened, such as the engine exploding into pieces and taking the transmission with it. But for a blown head gasket? You don't even need to replace the torque converter, which is what couples the engines to the trans.

No matter what you did to the engine, probably it did not affect the transmission. Just put the new engine in, and if it shifts OK, don't worry about it.